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Purpose: PANoptosis is considered a novel type of cell death that plays important roles in tumor progression. In this study, we applied machine learning algorithms to explore the relationships between PANoptosis-related lncRNAs (PRLs) and head and neck squamous cell carcinoma (HNSCC) and established a neural network model for prognostic prediction., Methods: Information about the HNSCC cohort was downloaded from the TCGA database, and the differentially expressed prognostic PRLs between tumor and normal samples were assessed in patients with different tumor subtypes via nonnegative matrix factorization (NMF) analysis. Subsequently, five kinds of machine-learning algorithms were used to select the core PRLs across the subtypes, and the interactive features were pooled into a neural network model to establish a PRL-related risk score (PLRS) system. Survival differences were compared via Kaplan‒Meier analysis, and the predictive effects were assessed with the areas under the ROCs. Moreover, functional enrichment analysis, immune infiltration, tumor mutation burden (TMB) and clinical therapeutic response were also conducted to further evaluate the novel predictive model., Results: A total of 347 PRLs were identified, 225 of which were differentially expressed between tumor and normal samples. Patients were divided into two clusters via NMF analysis, in which cluster 1 had a better prognosis and more immune cells and functional infiltrates. With the application of five machine learning algorithms, we selected 13 interactive PRLs to construct the predictive model. The AUCs for the ROCs in the entire set were 0.735, 0.740 and 0.723, respectively. Patients in the low-PLRS group exhibited a better prognosis, greater immune cell enrichment, greater immune function activation, lower TMB and greater sensitivity to immunotherapy., Conclusion: In this study, we established a novel neural network prognostic model to predict survival and identify tumor subtypes in HNSCC patients. This novel assessment system is useful for prediction, providing ideas for clinical treatment., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

In this work, we develop a method for learning interpretable, thermodynamically stable and Galilean invariant partial differential equations (PDEs) based on the conservation-dissipation formalism of irreversible thermodynamics. As governing equations for non-equilibrium flows in one dimension, the learned PDEs are parameterized by fully connected neural networks and satisfy the conservation-dissipation principle automatically. In particular, they are hyperbolic balance laws and Galilean invariant. The training data are generated from a kinetic model with smooth initial data. Numerical results indicate that the learned PDEs can achieve good accuracy in a wide range of Knudsen numbers. Remarkably, the learned dynamics can give satisfactory results with randomly sampled discontinuous initial data and Sod's shock tube problem although it is trained only with smooth initial data. [ABSTRACT FROM AUTHOR]

In this paper, we take a data-driven approach and apply machine learning to the moment closure problem for the radiative transfer equation in slab geometry. Instead of learning the unclosed high order moment, we propose to directly learn the gradient of the high order moment using neural networks. This new approach is consistent with the exact closure we derive for the free streaming limit and also provides a natural output normalization. A variety of benchmark tests, including the variable scattering problem, the Gaussian source problem with both periodic and reflecting boundaries, and the two-material problem, show both good accuracy and generalizability of our machine learning closure model. • We apply machine learning to the moment closure for the radiative transfer equation. • We propose to directly learn the gradient of the moment using neural networks. • The approach is consistent with the closure we derive for the free streaming limit. • The approach also provides a natural output normalization. [ABSTRACT FROM AUTHOR]

• We propose a data-driven method to discover multiscale chemical reactions governed by the law of mass action. • We propose a partial-parameters-freezing (PPF) technique to learn the multiscale reactions. • We use a single matrix to represent the stoichiometric coefficients for a system without catalysis reactions. In this paper, we propose a data-driven method to discover multiscale chemical reactions governed by the law of mass action. First, we use a single matrix to represent the stoichiometric coefficients for both the reactants and products in a system without catalysis reactions. The negative entries in the matrix denote the stoichiometric coefficients for the reactants and the positive ones for the products. Second, we find that the conventional optimization methods usually get stuck in the local minima and could not find the true solution in learning the multiscale chemical reactions. To overcome this difficulty, we propose a partial-parameters-freezing (PPF) technique to progressively determine the network parameters by using the fact that the stoichiometric coefficients are integers. With such a technique, the dimension of the searching space is gradually reduced in the training process and the global minima can be eventually obtained. Several numerical experiments including the classical Michaelis–Menten kinetics, the hydrogen oxidation reactions and the simplified GRI-3.0 mechanism verify the good performance of our algorithm in learning the multiscale chemical reactions. The code is available at https://github.com/JuntaoHuang/multiscale-chemical-reaction. [ABSTRACT FROM AUTHOR]